Question

The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $17,672. Assume that the standard deviation is =$2,705. Use z-table.

a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $162 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.

n=30 ______

n=50______

n=100_____

n=400_____

b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.

A larger sample increases probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within + or - 162 of u of  ranges from ______ for a sample of size 30 to ______ for a sample of size 400.

Answer 1

Ans:

a)

z=162/(2705/sqrt(n))

P(-z<Z<z)=P(Z<z)-P(Z<-z)

n	z	P(-z<Z<z)
30	0.328	0.2571
50	0.423	0.3281
100	0.599	0.4508
400	1.198	0.7690

b)A larger sample increases probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within + or - 162 of u of  ranges from 0.2571 for a sample of size 30 to 0.7690 for a sample of size 400.

b)